The absent tabs does seem like some sort of bug, but I’m not able to easily reproduce it here. If you can give me repeatable steps to cause this to happen, I’ll take a look.
Regarding the tab appearance issues, we are working towards removing our own tabbed UI interface in favour of the one Apple provides in macOS Sierra for future versions of Script Debugger. I doubt we’ll be able to provide font size settings, but Apple’s tabbed UI will probably be more rebate than the one we have now.
Open several documents in separate tabs in the same window, say about 5 or 6.
Open one or more new, untitled tabs in the same windo
Observe that the untitled tabs do NOT show in the tab list at the top of the window.
Because of the many bugs/issues that Sierra causes, some of us are staying with El Capitan (or even earlier macOS versions).
I would hope that you would release an update to SD6 using the current tab scheme that addresses the readability issue. Surely it is not that hard to adjust the text contrast and provide a preference setting for font size.